Transcript Law v. Theory

Observation,
Measurement
and Calculations
Cartoon courtesy of NearingZero.net
Steps in the Scientific Method
1.
Observations
- quantitative
- qualitative
2.
Formulating hypotheses
- possible explanation for the
observation
3.
Performing experiments
- gathering new information to
decide
whether the hypothesis is valid
Outcomes Over the Long-Term
Theory (Model)
- A set of tested hypotheses that
give an
overall explanation of some
natural phenomenon.
Natural Law
- The same observation applies to
many
different systems
- Example - Law of Conservation
of Mass
Law vs. Theory
 A law summarizes what happens
 A theory (model) is an attempt
to explain why it happens.
Nature of Measurement
Measurement - quantitative
observation
consisting of
2 parts
Part 1 - number
Part 2 - scale (unit)
Examples:
20 grams
6.63 x 10-34 Joule seconds
Systems of measurement
Metric system vs English system
»Metric (SI) International system
–Standardized
-international
–consistent base units
–multiples of 10
»English (US) system
–non-standard
-only US
–no consistent base units
–no consistent multiples
Using the Metric system
Prefixes for multiples of 10
»T - G - M -k h d (base) d c m -  - - n - -p
»Tera 1012 – Giga 109 – Mega 106 – kilo
103 – hecto 102 – deka 10 1 – base –
deci 10-1 – centi 10 –2 - milli 10 –3 –
micro 10 –6 – nano 10 –9 – pico 10 -12
»move the decimal to convert
The Fundamental SI Units
Physical Quantity
Name
Abbreviation
Mass
kilogram
kg
Length
meter
m
Time
second
s
Temperature
Kelvin
K
Electric Current
Ampere
A
mole
mol
candela
cd
Amount of Substance
Luminous Intensity
SI Prefixes
Common to Chemistry
Prefix
Unit Abbr.
Exponent
Kilo
k
103
Deci
d
10-1
Centi
c
10-2
Milli
m
10-3
Micro

10-6
Moving the decimal
For measurements that are defined by a single unit
such as length, mass, or liquid volume and later in
the course, power, current, voltage, etc., simply move
the decimal the number of places indicated by the
prefix.
400400 m
m == ??40,000
cm
cm cm
g
7755 mg = ?0.075
g
mm
0.025 m = ?0.000025
mm
Converting measurements
Metric
–
–
–
–
English
–
–
–
Metric
multiples of 10
move decimal
*area - move twice
*volume - move three times
Metric
conversion factors
proportion method
unit cancellation method
Common Conversions
1 kilometer = .621 miles
1 meter = 39.4 inches
1 centimeter = .394 inches
1 kilogram = 2.2 pounds
1 gram = .0353 ounce
1 liter = 1.06 quarts
Uncertainty in Measurement
A digit that must be estimated is
called uncertain. A measurement
always has some degree of uncertainty.
Why Is there Uncertainty?
 Measurements are performed
with instruments
 No instrument can read to an
infinite number of decimal places
Precision and Accuracy
Accuracy refers to the agreement of
a particular value with the true value.
Precision refers to the degree of
agreement among several
measurements made in the same
manner.
Neither
accurate nor
precise
Precise but not
accurate
Precise AND
accurate
Rules for Counting Significant
Figures
Nonzero integers always count as
significant figures.
3456 has
4 sig figs.
Rules for Counting Significant
Figures
Zeros
-
Captive zeros always count as
significant figures.(zeros in
between nonzeros)
16.07 has
4 sig figs.
Rules for Counting Significant
Figures
Zeros
- Leading zeros do not count as
significant figures.
0.0486 has
3 sig figs.
Rules for Counting Significant
Figures
Zeros
Trailing zeros are significant only
if the number contains a decimal
point.
9.300 has
4 sig figs.
Rules for Counting Significant
Figures
Any whole number that ends in zero
and does not have a decimal in
unclear or unknown.
10 unknown
20. Has 2 significant figures
Sig Fig Practice #1
How many significant figures in each of the following?
1.0070 m 
5 sig figs
17.10 kg 
4 sig figs
100,890 L 
unclear
3.29 x 103 s 
3 sig figs
0.0054 cm 
2 sig figs
3,200,000 
unclear
Rules for Significant Figures in
Mathematical Operations
Multiplication and Division: #
sig figs in the result equals the
number with the least number
of sig figs.
6.38 x 2.0 =
12.76  13 (2 sig figs)
Sig Fig Practice #2
Calculation
Calculator says:
Answer
3.24 m x 7.0 m
22.68 m2
100.0 g ÷ 23.7 cm3
4.219409283 g/cm3 4.22 g/cm3
23 m2
0.02 cm x 2.371 cm 0.04742 cm2
0.05 cm2
710 m ÷ 3.0 s
236.6666667 m/s
unclear
1818.2 lb x 3.23 ft
5872.786 lb·ft
1.030 g ÷ 2.87 mL
2.9561 g/mL
5.87 x 103 lb·ft
2.96 g/mL
Rules for Significant Figures in
Mathematical Operations
Addition and Subtraction: The
number of decimal places in the
result equals the number of
decimal places in the number
with the least decimal places.
6.8 + 11.934 =
18.734  18.7 (3 sig figs)
Sig Fig Practice #3
Calculation
Calculator says:
Answer
3.24 m + 7.0 m
10.24 m
10.2 m
100.0 g - 23.73 g
76.27 g
76.3 g
0.02 cm + 2.371 cm
2.391 cm
2.39 cm
713.1 L - 3.872 L
709.228 L
709.2 L
1818.2 lb + 3.37 lb
1821.57 lb
1821.6 lb
2.030 mL - 1.870 mL
0.16 mL
0.160 mL
Significant Figures
Rules for rounding off numbers
(1) If the digit to be dropped is
greater than 5, the last retained
digit is increased by one. For
example,
12.6 is rounded to 13.
(2) If the digit to be dropped is less
than 5, the last remaining digit is left
as it is. For example,
12.4 is rounded to 12.
(3) If the digit to be dropped is
5, and if any digit following it is
not zero, the last remaining digit
is increased by one. For example,
12.51 is rounded to 13
Significant Figures
(4) If the digit to be dropped
is 5 and is followed only by
zeros, the last remaining digit
is increased by one if it is
odd, but left as it is if even.
For example,
11.5 is rounded to 12,
12.5 is rounded to 12. This rule
means that if the digit to be
dropped is 5 followed only by
zeros, the result is always
rounded to the even digit. The
rationale is to avoid bias in
rounding: half of the time we
round up, half the time we round
down.
Scientific Notation
In science, we deal with some very
LARGE numbers:
1 mole = 602000000000000000000000
In science, we deal with some very
SMALL numbers:
Mass of an electron =
0.000000000000000000000000000000091 kg
Imagine the difficulty of calculating
the mass of 1 mole of electrons!
0.000000000000000000000000000000091 kg
x 602000000000000000000000
???????????????????????????????????
Scientific Notation:
A method of representing very large or
very small numbers in the form:
M x 10n
 M is a number between 1 and 10
 n is an integer
.
2 500 000 000
9 8 7 6 5 4 3 2 1
Step #1: Insert an understood decimal point
Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form M x 10n
2.5 x
9
10
The exponent is the
number of places we
moved the decimal.
0.0000579
1 2 3 4 5
Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form M x 10n
5.79 x
-5
10
The exponent is negative
because the number we
started with was less
than 1.
Direct Proportions
 The
quotient of two
variables is a constant
 As the value of one
variable increases, the other
must also increase
 As the value of one
variable decreases, the
other must also decrease
 The graph of a direct
proportion is a straight line
Inverse Proportions
 The
product of two
variables is a constant
 As the value of one
variable increases, the
other must decrease
 As the value of one
variable decreases, the
other must increase
 The graph of an inverse
proportion is a hyperbola